(2019-10-05, 10:34 PM)Chris Wrote: Here's another from the Skeptical Intelligencer:
‘You know’, said the historian, ‘it never ceases to amaze me that of the first five presidents of the USA, three died on the fourth of July’. ‘Really?’ exclaimed both the psychologist and the mathematician. ‘Yes’, the historian continued, ‘and what are the odds of your correctly guessing which three they are?’ After a short pause the psychologist answered, ‘One in six’. ‘Hang on’, said the mathematician as he jotted down his calculations on a scrap of paper. ‘It’s actually one in ten’. Who is right?
My wary solution:
Show contentSpoiler:
It seems to me that this is a simple combinatorics problem, and that the answer is one in 5C3, or 1 in (5x4x3)/(3x2x1) = 1 in 10. But I don't see how somebody could get one in six, so I don't see why that answer is wrong other than that this one is right, and thus am wary that I have missed something and fallen into a trap.
For bonus points: complete the same nine-ball puzzle as above but for 12 balls instead of nine. That is, everything about the puzzle description is the same, except that there are 12 balls instead of nine. For double bonus points: provide a solution with unconditional weighings (along the lines of the final answer for nine balls which I provided in an above post).
(2019-10-05, 10:34 PM)Chris Wrote: Here's another from the Skeptical Intelligencer:
‘You know’, said the historian, ‘it never ceases to amaze me that of the first five presidents of the USA, three died on the fourth of July’. ‘Really?’ exclaimed both the psychologist and the mathematician. ‘Yes’, the historian continued, ‘and what are the odds of your correctly guessing which three they are?’ After a short pause the psychologist answered, ‘One in six’. ‘Hang on’, said the mathematician as he jotted down his calculations on a scrap of paper. ‘It’s actually one in ten’. Who is right? The question contains superfluous information. Here is a simpler version:
‘You know’, said the historian, ‘it never ceases to amaze me that of the first five presidents of the USA, three died on the fourth of July’. ‘Really?’ exclaimed both the psychologist and the mathematician. ‘Yes’, the historian continued, ‘and what are the odds of your correctly guessing which three they are?’ After a short pause the psychologist answered something. ‘Hang on’, said the mathematician as he jotted down his calculations on a scrap of paper. ‘It’s something else’. Who is right?
(2019-10-06, 05:18 AM)Beasty Wrote: The question contains superfluous information. Here is a simpler version:
‘You know’, said the historian, ‘it never ceases to amaze me that of the first five presidents of the USA, three died on the fourth of July’. ‘Really?’ exclaimed both the psychologist and the mathematician. ‘Yes’, the historian continued, ‘and what are the odds of your correctly guessing which three they are?’ After a short pause the psychologist answered something. ‘Hang on’, said the mathematician as he jotted down his calculations on a scrap of paper. ‘It’s something else’. Who is right?
But now the question is unanswerable!
(2019-10-06, 05:38 AM)Laird Wrote: But now the question is unanswerable!
Perhaps we need to know whether Beasty is a mathematician or a psychologist.
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(2019-10-06, 12:49 AM)Laird Wrote: My wary solution:
Show contentSpoiler:
It seems to me that this is a simple combinatorics problem, and that the answer is one in 5C3, or 1 in (5x4x3)/(3x2x1) = 1 in 10. But I don't see how somebody could get one in six, so I don't see why that answer is wrong other than that this one is right, and thus am wary that I have missed something and fallen into a trap.
Yes - it is a trick question, and I fell into the trap too.
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The psychologist is reasoning that (unless the historian is being deliiberately misleading) he wouldn't have specified the first five presidents unless the fifth president was one of the three. Therefore it reduces to the problem of guessing the other two correctly from among the first four.
Remarkably, the second and third presidents died not only on the same day of the year, but on the same date - the fiftieth anniversary of Independence.
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• Laird
(2019-10-06, 07:03 AM)Chris Wrote: Perhaps we need to know whether Beasty is a mathematician or a psychologist.
Messing with our minds => psychologist, of course!
(This post was last modified: 2019-10-06, 07:44 AM by Laird.)
(2019-10-06, 07:21 AM)Chris Wrote: Yes - it is a trick question, and I fell into the trap too.
Dang. We'll get you next time, Skeptical Intelligencers!
This one is maybe too easy and well-known, but it's one of my favorites to do with my students...
A windowless attic contains three identical light fixtures, each containing an identical light bulb. Each light is connected to one of three switches in the basement. Each bulb is switched off at present. You are in the basement with the three switches.
Before walking up to the attic, you have 15 minutes in the basement to touch the switches. But once you've left the basement, you may no longer touch a switch. After this, you go directly upstairs to the attic and must identify which light fixture goes with which switch.
How can you tell which switch goes with which light?
My take on the trick.
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So the question isn't "who is right?", but "how did the psychologist come up with one in six?" Because even with the given explanation, the mathematician should still be considered right...maybe? Yes, people do tend to stop on the last event included when they say "5 of the top 8". But not always, especially if you're talking about a "top 10". And there are puzzles out there where the "trick" is to not make the assumption the psychologist made. For example, "how many months have 28 days?"
I guess the right answer is supposed to be the one which the most people miss, in these puzzles. Which makes the psychologist right.
Linda
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